Negative impedance repeaters



April 17, 1956 J. L. MERRILL, JR

NEGATIVE IMPEDANCE REPEATERS Original Filed Aug. 30, 1949 5 Sheets-Sheet 1 J. L. MERRILL, JR.

A T TORNEY p i 7, 1956 J. MERRILL, JR 2,742,616

NEGATIVE IMPEDANCE REPEATERS Original Filed Aug. 50 1949 5 Sheets-Sheet 2 y J. L. M'RR/LL, JR.

ATTORNEY April 1956 J. L.MERRILL, JR 2,742,616

NEGATIVE IMPEDANCE REPEATERS Original Filed Aug. 30, 1949 5 Sheets-Sheet 3 A T TORNE) April 17, 956 J. 1.. MERRILL, JR 3 3 NEGATIVE IMPEDANCE REPEATERS Original Filed Aug. 30, 1949 5 Sheets-Sheet 4 FIG. .9

: FIG. /0 -J F/G. I i

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R m P M "M -20 R 1 32 X 20 2 10 z/ a 1.: TV F G. /4 o W Al 1 13 R M L i O lNVEN TOR J. L. MERR/LLJR.

A T TORNEV 1 2,742,616 NEGATIVE IMPEDANCE REPEATERS Josiah L. Merrill, Jr., Port Washington, N. Y., assignor "to Bell Telephone Laboratories, Incorporated, New

York, N. Y., a corporation of New York Original application August 30,- 1949, SerialNo. 113,072,

I now Patent No. 2,582,498, dated January 15, 1952. Divided and this application October 23, 1950, Serial No. 191,670 i Y 10 Claims. 01. ass-4:0

This invention relates to negative impedance circuits such as, for example, negative impedance converters, negative impedance repeaters and circuits incorporating them, and transmission lines loaded with negative impedances.

Objects of the invention are production of stable negative impedance, and reduction of attenuation or distortion in transmission lines.

It is also an object of the invention to provide a stable transmission system comprising a vacuum tube type of negative impedance repeater connected in series between two inductively loaded lines or in series between an inductively loaded line and a non-loaded line;

The present application is a division of application Serial No. 113,072, filed August 30, 1949 .(issued January 15, 1952, as United States Patent 2,582,498).

In one aspect the invention is a specific form of vacuum tube negative impedance converter, i. e., vacuum tube circuit for converting-positive impedance into negative impedance. The practical (i. e., real or actual) converter is reducible to an electrically equivalent four-terminal circuit consisting of positive impedance elementstogether with a device that may be referred to as an ideal negative impedance converter. Thev ideal negative impedance converter is a four-terminal network or device that has an impedance transformation ratio of k: 1, k being a quantity that is a numeric at a prescribed frequency and ap- 1 proximately a numeric over a finite frequency range which includes the prescribed frequency, but that at frequencies below and above this range-is a complex quantity which can have an appreciable phase angle. .In the Cfirst-mentioned equivalent circuit, some of the positive impedance elements appear as a network on one sideof the ideal converter; the remainder appear as a network on the other side of the ideal converter. These two networks tend to make the ratio of impedance transformation for the prac&

tical converters equivalent circuit for the ideal converter. 1

In accordance with a feature of the invention, the practical converter can be so constructed that, except with regard to power dissipation, the two networks in its equivalent circuit substantially. balance each other in eifect over the frequency range of interest.. Thus only the etfectof the ideal converter remains and the practical converter can be represented by the ideal converter.

In accordance with a feature of the invention, tofacilitate obtaining this balance or to reduce the elfect of unbalance of the two networks, the impedance of series arms of the networks may be made relatively low'and the im pedance of shunt arms relatively high.

In accordance with a feature of the invention, the converter is constructed to develop a negative impedance over a prescribed frequency range and positive impedance outside this frequency range. Such impedance control is desirable for a number of reasons. For example, :at'extremely high or low frequencies the positive impedance elements of the converter determine the impedance seen at its terminals. For many practical purposes, it is not only necessary to have the" impedance seen at the termidepart from the ratio nals negative over a prescribed range of frequencies, which is the range of primary interest, but it is also necessary to have the impedance seen at the terminals positive at frequencies outside this band. A positive impedance at high and low frequencies may be desired for two reasons: first, to insure stability against oscillation; and second, to attenuate or pass other signals at frequencies where gain may not be wanted. For example, in a telephone line gain may be required for the'voice band of frequencies, but'not wanted at the lower frequencies of ringing, dialing, and the like. The reason for this is'that the power handling capacity required of a negative impedance converter to increase ringing and dialing' currents would have to be much greater than that required to provide gain for speech currents only. Ringing generators or dial pulse repeaters might prove more economical. for supplying power at these lower'frequencies. i

One specific form. of negative impedance converter embraced by the inventionis an electric space discharge amplifier comprising a negative feedback impedance common to the cathode-anode and cathode-grid circuits and adapted to serve as an input coupling circuit and output coupling circuit for the amplifier, an anode circuit load impedance in serial relationwith the feedback impedance in the cathode-anode circuit, and means for producing in the amplifier positive feedback that renders the amplifier input impedance negative over a prescribed frequency range, the means for producing positivefeedback' comprising a positive feedback path whose input voltage depends upon and is derived from the anode circuit load impedance. The negative feedback reduces the amplifier input impedance to a. low'value and the positive feedback further reduces it, rendering it negative over the prescribed frequency range. The anode circuit load impedance includes an impedance network for controlling the magnitude and phase of the amplifier input impedance, in order, for example, to give gain control and attenuation equal ization when the'converteris connected as a'repeater in series in a telephonetransmission line. The repeater, while of general utility, is particularly suitable for use in exchange area circuits. of telephone systems, where gain with stability against oscillation is difficult to obtain because the impedances encountered byrepeatered line's vary-widely as a result of the great variety of facilities to be interconnected orswitched.

Other objects, aspects and features of the invention will be apparent from theafollowing description andrclaims.

Fig. 1 shows a basic or ideal negative impedance converter;

Fig. 2 shows the impedance seen at terminals 1 of the idealconverter; i

Fig. 3 shows the impedance seen at terminals 2 of the ideal converter; 1

Fig. 4 shows the equivalent circuit of a practical converter;

Figs. 5 and 6 show the circuit schematic and equivalent circuit respectively,- of a practical negative impedance converter, and Fig. 5A shows the'circuit'of Fig. 5 with its triodes'represented by their equivalent circuits;

Figs. 7 and 8 show the circuit schematic and equivalent circuit of another practical negative impedance converter, and Fig. 7A shows a modification of the circuit of Fig. 7;

Fig. 9 shows the impedance characteristic plotted in polar form as seen at terminals 1 of Fig. 7 with a resistance connected to, terminals 2; v

Figs. 10 and 11 show converters respectively in series and in shunt with a line;

Figs. 12, 13 and 14 show networks for use with a negative impedance converter connected in series with a transmission line; I

c Fig. 15 shows a negative impedance repeater in series between inductively loadedline sections;

practical converter.

planation of Figs.

Fig. 17 shows a negative impedance repeater in series between an inductively loaded line and a non-loaded line; and

Fig. 18 shows an impedance network for use in the repeater in Fig. 17.

Fig. 1 presents an ideal negative impedance converter -C. It is :a form of transformer but has a .negative ratio of impedance transformation :or conversion designated k:1, as shown. Like a transformer, the converter C can have four terminals. It iscapable of bilateral transmission. As shown in Fig. .2, if .a positive impedance Zn is connected to terminals 2, kZN is seen at terminals 1. As shown in Fig. .3, .if .a positive impedance ZN is connected to terminals '1, Zn/k is seen at terminals 2. As noted by G. Crisson (Negative Impedance and the Twin 2-l-Type Repeater-B. 'S. T. I.July 1'93 1) there are two types of negative impedance, the series type and the shunt type. It is desired to point out the fact that if impedance is defined as .Z'=E/ I then negative impedance can be either Z multiplied by -1, (i. c., Z

negative impedance seen at terminals 1, Fig. 2, is the lent-circuit along withthe ideal converter. This is illustrated by Fig. 4, which shows the equivalent circuit of a Some of these positive impedance elements appear asalnetwork N1 on'the left-hand side of the ideal converter; the others appear as a network N2 on the right-hand side. and N2 are such that they tend to make the ratio of transformation for the practical converters equivalent circuit depart from the ratio for the ideal converter. If networks N1 and N2, when viewed from the converter C, had the same configuration and had the impedanceof each element in N1 equal k times the impedance of the cor respondingly located elemnet in N2, then (except with regard to .power dissipation) these networks N1 and N2 would balance each other in effect, thus cancelling-out, so only the effect of the idealconvertcr would remain and Fig. 4 could be represented by Fig. 1; or in other words, then the practical converter would be such that in its equivalent circuit each of the networks N1 and N2 as seen from the other (through the ideal converter) would neutralize the effect of the-other (upon the transformation ratio .of the equivalent circuit of the practical converter), and so the impedance transformation ratio for the practical converter would be the same as for the ideal converter. As can be seenfrom Figs. Sand 6, described below, difiiculty might be encountered were it attempted to make the practical converter such thatN1 and N2 in its equivalent circuit would, when viewed from C, have like configurations and havethe impedancecf each element in N equal k times the impedance of the correspondingly located element in N2, (for example, were it attempted to add to each network the-elements required for giving it the same configuration as the other network when the two networks are viewed from C, and then assign each element in N1 an impedance value equal to k times that of the correspondingly located element in N2). However, in accordance with a hereinafter described feature of the invention, the practical-converter can be readily made such that, inits equivalent circuit, over the frequency range of interest N1 and N2 mutually substantially cancel or neutralize their effects on the transformation ratio. This can be accomplished by constructing the practical converter so that in the networks N1 and N2 of its equivalent circuit the following conditions obtain over the frequency range of interest: (1') certain of the series and shunt elements have their impedances Ordinarily these networks N1 low and high, respectively, compared to each of the two impedances between which the converter is to be connected, so the effects of those series and shunt elements on the impedance transformation ratio of the equilavent circuit of the practical converter are negligibly low; and (2) the remaining elements (of the networks N1 and N2) have their impedances and their positions in the network configurations such that the remaining elements in each network substantially cancel or neutralize the effect of the remaining elements in the other network upon the over-all transformation ratio of the equivalent circuit of the practical converter.

Fig. 5 shows the circuit schematic of a practical negative impedance converter embodying one specific aspect of the invention. It comprises: two transformers designated T and T2; two identical vacuum tubes or electric space discharge devices preferably normally biased for class A operation, each designated V1; two similar capacitors designated C1, each capacitor .coupling the plate of one tube to the grid of the other, for producing positive feedback; two similar resistors R1, respectively connecting the grids of the tubes to the negative terminal of the battery B; and two resistors R2, one in each cathode circuit, for grid bias. The negative pole of the battery B is shown grounded. The devices V1 are in push-pull relation. One winding of transformer T1 is connected in series with the resistors R2 between the cathodes and has its mid-point grounded. The resistors R2 and the two halves of this winding produce negative feedback and produce direct-current voltage drops for biasing the grids of the two tubes equally. The direct-current resistance of one of the halves of the winding may exceed that of the other half by a given amount, and then the resistance of the element R2 adjacent that other half may exceed by the same amount the resistance of the other element R11. The devices V1 may be, for example, twin triodes of a Western Electric type 407A vacuum tube, which has the amplification constant a of each triode equal to approximately 30.

While the discharge devices shown in Fig. 5 (and those shown in Fig. 7 which is described hereinafter) have but one grid, the term triode in the specification and claims is generic to multigrid discharge devices, for example, tetrodcs and pentodes which include a cathode, an anode and a grid 'or space discharge control element.

Let n represent the amplification from the platc-toground voltage of either vacuum tube to the resulting component of the internal plate-cathode generator voltage in the other tube, and let ,uz represent the amplification from the cathode-to-ground voltage of either tube to the resulting component of the internal plate-cathode generator voltage in the tube. Thus, 2 is the factor by which the voltage between cathode of either tube and ground (or the negative pole of the battery B) must be multiplied in order to obtain the value of the resulting component of internal plate generator voltage in that tube, (or in other words, 2 is the tube amplification constant, usually designated ,u); and 11 is the quantity by which the voltage between the plate of either tube and ground (or the negative pole of the battery B) must be multiplied in order to obtain the component of internal plate generator voltage of the other tube that results from the voltage drop between its grid and ground. The amplification factor 1 is equal to flaz where ,8 designates the ratio of the voltage between ground and the grid of either tube to the voltage between ground and the plate of the other tube. Representing the triodes by their equivalent circuits in conventional manner, the circuit of Fig. 5 can be reduced to that of Fig. 5A. In Fig. 5A, the voltage between ground and the cathode of one tube is designated en, the voltage between ground and the plate of the other tube is designated 01, and the voltage across the resistor R1 in the grid circuit of that other tube is designated es. The plate generator in the one tube is indicated as two generators in series, one be ing designated by its voltage ezand the other being designated by its voltage [283, the total plate generator voltage in this tube being ,uez-l-nes. It is seen that .where w designates the angular velocity in radians.

Thus, ,ui, the amplification of the voltage in the plate circuit, depends upon the relative values of C1 and R1 In addition, the internal plate resistance of the tubes appears as an impedance in series with transformer T1,

this impedance being shown as a resistance of value the value of the plate resistance in each tube being taken as Rp. -If ,u1 approximates ,u2 and each is much greater than unity, k approximates unity. If K l and is of small order of magnitude relative to the impedance that it'faces (i; e., relative to the sum of all impedances effectively in series with it), then the action of the converter, to a first approximation at least, is independent of minor variations in tube constants and battery supply voltage. Making 2 large and Rp small tends to reduce the impedance of the element identified in the drawing as '2Rp/(l'+,u2) and thus render its effect on the negative impedance presented by the converter unimportant. In the circuit of Fig. 6, all elements on the left-hand side .of the ideal converter C may be designated as a network N1 and all elements on the right-hand side of the ideal converter C may be designated as a network N2, after the fashion of Fig. 4. As indicated above, it i apparent that difficulty would be encountered were attempt made to so construct the circuit of Fig. 5 that in its equivalent circuit shown in Fig. 6, N1 and N2 when viewed from C would have the same configuration and have the impedance of each element in N1 equal k times the impedance of the correspondingly located element in N2. a

However, if all series elements in the circuit of Fig. 6 can be made relatively small in impedance and all shunt elements relatively large the circuit will approach that of the ideal converter. In other words, the operation or effect of the circuit approaches that of the ideal converter provided that, when the transformer T1 and T2' are. replaced by their usual equivalent networks, all impedances (of elements of networks N1 and N2) effectively in series in the circuit with respect to transmission between terminals 1 and 2 are much smaller than each of the two impedances to be attached to terminals -1 and 2, and all impedances effectively in shunt across the drcuit with respect to transmission between terminals 1 and 2 are much greater than each of the just-mentioned two impedances. At high frequencies a practical difiiculty arises. The windings of transformers T1 and T2 have distributed capacity and leakage inductance. At somefrequency this capacity and inductance will resonate. If this frequency is not identically the same for T1 and T2, the circuit may be unstable and oscillate as explained below. A converter of the type described herein is essentially a feedback amplifier and as such must meet Nyquists rule for stability (given in the article by H. Nyquist ori Regeneration Theory, B. S. T. 1., January 1932). However,,,with reference to the ideal converter there is a similar rule which can be applied in order to determine unconditional stability. Referring to the ideal converter of Fig. 2, assume a line or other circuit of impedance Z1..(n0t shown in Fig. 2) is connected to terminals 1. Then if kZN-were equal to Z1. it is evident that the impedconverter provided that, when the transformers T1 and ance of the circuit mesh consisting of ZL-kZN would be zero and oscillationor singing would occur. Thus, it becomes evident that kZN should not equal Zn; or, what is the same thing, the ratio kZN/ZL should not equal 1/0 if the system is to be stable. Furthermore it can be shown that for an ideal converter the ratio kZN/ZL is the feedback factor, (#13 as defined on page 32 of H. W. Bodes book on network analysis and feedback amplifier design, published by D. Van- Nostrand Company, New York), of the amplifier in the converter. In view of this fact, Nyquists rule for stability in feedback amplifiers can be paraphrased as follows: for stability to obtain in an ideal negative impedance converter the locus of the ratio -kZN/Zr. over the frequency range from zero to infinity must not enclose the point l/O.

From a practical engineering viewpoint there is a criterion for judging "stability which is often more useful than the general rule. It can be stated as follows: The ideal negative impedance converter will be unconditionally stable providing that the magnitude of kZN/ZL is less than unity at any frequency where the angle of this ratio is zero.

In a practical converter, as shown in Figs. 4, 5 or 6, thesame rule for stability holds except Zr. is to be taken as the impedance seen looking toward network N1 from the ideal converter C and ZN is to be taken as the imped- -ance seen looking toward network N2 from the ideal converter C. If the elements in N2 are all made equal to or less than l/k times corresponding elements in N1 in impedance at all frequencies, then these two networks can be omitted from stability considerations for many practical purposes. Otherwise, the efiect of N1 must be 7 included in Z1. and the effect of N2 must be included in ZN, in applying the stability rule. If at any frequency a resonant-condition then exists whereby the impedance ZN goes to a high value there will be the possibility of kZN being greater than Zr... If when this condition occurs the angle of the ratio kZN/ZL is zero the circuit may oscillate. Therefore, it is desirable to prevent such resonance from occurring in the network N2 of Fig. 4.

One way of accomplishing this is illustrated in Figs. 7 and 8. The Fig. 7 is similar to Fig. 5 except that a retard coil or inductancecoil L2 has been substituted for transformer T2, resistor R3 has beeninserted in series with capacitor C1, and capacitor C2 has been shunted across R1. The network C1, R3 and R1 largely determines the value of 1.1 at low frequencies. The network R3, R1 and C2 largely determines the value of ,u1 at high frequencies. (As in the case of Fig. 5, 2: and ,ur is the amplification from the plate-to-ground voltage of either triode to the resulting component of the internal plate-cathode generator voltage in the other triode. The

equivalent circuit of Fig. 7 has been derived by application of circuit theory and is shown in Fig. 8. On the right-hand side of the ideal converter C all reactance elements are in shunt paths across the terminals 2. An antiresonance' can occur but in any such case the impedance on the right-hand side of the ideal impedance converter will be determined primarily by the network attached to terminals 2. It is an important feature of Fig. 7 that in itsequivalent 'circuitshown as Fig. 8, in the circuit between the ideal converter C and the terminals 2 there is no impedance effectively in series that might, by resonating with capacitance effectively in shunt across the circuit, cause the impedance on the right-hand side of C to be greater than that on the left-hand side and thereby create possibility of instability or singing. In Fig. 6, in contrast, leakage inductanceof transformer T2, effectively in series in the circuit between the ideal converter 'C and the terminals 2, might resonate 'at a high frequency with shunt capacitance (distributed capacitance of windings of T2) and thus 'forman antiresonant circuit (including ZN) .across the right-hand terminals of con verter C, and thereby cause the impedance on the righthand side of converter C to exceed 'l/k times that on the left-hand side (and so create a potential singingconditionthat would require careful consideration in the design of theconverter and its associated circuits).

'In Fig. 8, as in Fig. 6, the ratio of transformation -k equals -'(/1l""1)/([.L2+1), where 1 depends upon the values of the impedances in the RC circuit coupling the grids and plates of the vacuum tubes (aswell as upon the amplification factor of the tubesthemselves). At high and low frequencies, n1 is not a numeric but is a complex quantity whose angle and magnitude are determined at these frequencies largely by the values of the justmentioned impedances. In the operating frequency range, if these impedance values are adjusted so n approximates ,u.2 and each is much greater than unity, -k approximates unity. If, over a definite frequency band, all shunt elements in Fig. 8 are made relatively large and all series elements relatively small in value as referred to above in connection with Fig. 6, and, furthermore, 1;:1, then the circuit of Fig. 8 (and correspondingly the circuit of Fig. 7) approximates in operation on this frequency band an ideal converter having a ratio of transformation of -1 times the ratio of the impedance of the line winding of transformer T1 facing terminals 1 to the impedance of the other winding of transformer T1. If k is close to unity and the impedance Rp/ (1+ 2) is of small order of magnitude relative to the impedance that it faces, then battery supply variations and tube changes will have little effect upon the negative impedance presented by the converter. (As indicated above in connection with Fig. 6, making r2 large and Rp small, for example by appropriate choice of tube type and operating voltages, tends to render ZRp/(l-Hn) negligibly small.)

Negative resistance can be obtained only over a finite range of frequencies. For example, when a resistance (not shown) is connected to terminals 2 of Fig. 8, the impedance seen looking into terminals 1 resembles the locus shown on the polar diagram of Fig. 9. Between .a frequency f2 and a higher frequency f3, there is seen at terminals 1 an impedance which approximates a negative resistance, and at some frequencies between f2 and is a pure negative resistance is found. At zero frequency the impedance seen is a small positive resistance equal to the direct-current resistance of the primary winding of transformer T1. At a low frequency f1 the locus shows a positive impedance. The admittance corresponding to this portion of the impedance locus can be used, for

example when terminals 1 are in series in a telephone transmission line, for the passage of low frequency currents for ringing, dialing, and the like. At high frequencies ft the impedance locus approaches the origin, the impedance approaching zero through capacitive reactance. At high frequencies above the band passed by the telephone line, ordinarily it is desirable that the impedance be positive because gain at those high frequencies is not useful and may be detrimental in adding to the difficulty of obtaining stable operation. As explained hereinafter, when terminals 1 are used in series with a voice frequency transmission line, the impedance .most suitable for use across terminals .2 ordinarily will not be a pure resistance but will be a network presenting a complex impedance.

Between frequencies such as f2 and is the network across terminals 2 most accurately controls the negative impedance. Therefore, the main transmission band where negative impedance is desired, ordinarily will have its center between two such frequencies and preferably lie 'between them. For example, in the case of a converter employed in a voice frequency negative impedance repeater, the frequencieson its impedance locusthat corresponds to f2 and is may be 300 cycles per second and 4,000 cycles per second, respectively, and the phase angle of the negative impedance at each of these two frequencies may differ from 180 degrees by some five or ten degrees. Of course, gain can be had over a band wider than from 300 to 4,000 cycles per second if desired.

In one specific practical design of converter circuit of the type of Fig. 7, over the voice band of frequencies 1 is approximately equal to ,wz, and because 1 and #2 are large compared to unity the ratio of transformation of the converter equals about 0.9:1 at voice frequencies. The devices V1 are twin triodes of a Western Electric type 407A vacuum tube for which ,0. is approximately 30. The impedance ratio of the line transformer T1 is 1:9 step up from the line winding to the winding conductively connected to the cathodes. In the equivalent circuit of the converter, the shunt arms of the equivalent networks on each side of the ideal converter are high impedances at voice frequencies and can be neglected. To cancel the effect of the series resistances on the left-hand side of the ideal converter in this circuit, a series resistance l/k times as great (in this case about 2,000 ohms) is needed on the right-hand side of the ideal converter. In the practical circuit this resistance is added as shown at R4 in Fig. 7A, wherein block'71 is the same circuit as block 71 in Fig. 7. Thus, .in Fig. 7A, if a network Zn of impedance value ZN be connected across terminals 2, for example as indicated in Fig. 2 or in Figs. 10, ll, l5-or 17 described hereinafter, then at voice frequencies the impedance of terminals I viewed from the line equals approximately -0.1ZN. By inserting a resistance R4 such as that of Fig. 7 in the circuit-of Fig. 8, as a series element of the circuit, for example between the upper terminal 2 and the junction of C1 and L2; the circuit of Fig. 8 is so modified as to become equivalent to the circuit of Fig. 7A, and in such equivalent circuit the resistance R4 will be a part of the network N2, the network between the ideal converter C and the terminals 2. In such equivalent circuit, the network N2 is adapted to neutralize over a prescribed frequency range (the speech frequency range or the frequency range of interest) the effect of the network N1 on the over-all transformation ratio of the equivalent circuit of the converter. In such equivalent circuit the networks N1 and N2 have series and shunt impedance elements (transformer T1 may be replaced by its usual equivalent T network), certain of the series and shunt elements having their impedances low and high, respectively, compared to each of the two impedances between which the converter is to be connected (i. e., the impedance to be connected across terminals 1 and that to be connected across terminals 2), and the remaining impedance elements in the two networks N1 and N2 having their impedances such that the remaining elements in each network are adapted substantially to neutralize the effect of the remaining elements in the other network upon the over-all transformation ratio of the equivalent circuit of the practical converter of Fig. 7A (for example, the remaining element R4 in network N2 is equal to l/k times the sum of the resistance 2R2, the resistance quency range each shunt arm of the networks N1 and'Nz (including the shunt arm or item of the equiva'lent'T network of the transformer T1, the shunt arm comprising condensers C1, condensersCzz, resistance 2R1 and resistances R3 and the shunt arm L2) is of highimpedance compared to each of the two impedances between which the converter is to be connected, and the impedance of the series arms of the network N1 equals k times the impedance of the series arms of the network N2, or in 'other'words, R4 equals 1/k times the sum of 2R2, the resistance v ZRp 'andthe resistance-of. the series arms of the equivalent T network of the transformer T1, 1

v (is being M+ Inthe case of this equivalent network of the converter .of Fig. 7A, as in the caseof the equivalent network (Fig. 8) of the converter of Fig. 7, all reactance elements of the network N2 (including the condensers C1 and C2 and the inductance L2) are in shunt arms of that network, so all series arms of that network have negligible reactance or in other words that-network has no series arms whose reactanceis not-negligible. In the :case of the converters of Figs. 7 andS, the converter preferably is such that in its equivalent circuit (Fig. 6 with its transformers T1 and T2 considered to be replaced by their usual equivalent T networks, and Fig. 8 with its trans- .former T-1. considered to be replaced by the usualequivalent T network) the impedance of all series elements of thecircuit (between terminals 1 and ideal converter C and between C and terminals 2) is much smaller than the impedance to be attached to terminals 1 and than the impedance to be attached to terminals2, and the impedances of all shunt arms of the circuit (between C and terminals 1 and between C and terminals 2) are much greater thanthe impedance to be attached to terminals 1 andthe impedance to be attached to terminals 2.

, Converters embraced in the invention include not only converters of push-pull form but also converters of singlesided form, as for example, the converter (not shown) obtainable by omitting from Fig. 5, vthe following elements on the right-hand side of the fiigure: V1, C1, R1, R2 and the windingbetween R2 and ground. However, in the case of Fig. 5 the push-pull form has important advantages, including: double the power output of the single-sidedcircuit (assuming tubes of like type for the push-pull and the single-sided circuits); power supply =noise reduction due to push-pull operation; and especially theadvantages that ,ul is not dependent entirely upon the ,coupling factor between the two halves of the centertapped winding of transformer T2, and that the effect of the three-winding transformer.T2 upon the transformation ratio of the converter can much more readily be balanced out or neutralized by a push-pull (three-winding) transformer T1 than be the two-winding transformer which would result from omission of the winding between R2 and ground. In the push-pull form of the converter as shown in Figs. 5 and 6, over a prescribed frequency range k may, forexample, bemade close to unity as indicated above, the sum of the impedances 2R2 and from Fig. 7 the following elements: the right-hand tube V1, the resistance R2 at its cathode, the winding turns of transformer T1 connected 'hetween that resistance and ground, and the elements C1, R3, R1 and C2 that couple the plate of the left-hand tube to the-grid of the righthand tube. However, in contrast to this single-sided circuit, the corresponding push-pull form shown in Figs. 7 and 8 has the important advantages, especially the advantage that the positive feedback coupling through the coil L2 is supplemented by positive feed coupling from the plate of each tube to its grid through the other tube (acting as an amplifier in the regenerative feedback path). Thus the phase angle of #1 is not entirely dependent upon the coupling between the two halves of the winding of L2 as it would be in the single-sided arrangement. Furthermore, in the single-sided arrangement there would appear in its equivalent circuit a series rterrn between the terminals 2 and the ideal converter C which would depend in value upon the leakage inductance in L2. reactive and thence introduce th'epossibility of singing, as explained above.

Considering Fig. 7, for example, ashaving terminals -1 connected in series in a line and terminals 2 connected to a network ZN as shown in Fig. 10 described hereinafter, the converter may be viewed as a vacuum tube circuit with both negative feedback and positive feedback and with the terminals 1 serving as the input terminals and also the output terminals so the input impedance is also the output impedance. In each triode, negative feedback is produced by the impedance of the resistance R2 at its cathode and the winding turns of transformer T1 connected between that resistance and the negative pole of battery B. This negative feedback greatly lowers the impedance between the cathode and ground (somewhat as the feedback action in a cathode follower reduces its cathode-to-ground impedance). The lowering of the impedance between the cathode .of each triode V1 and ground results in lowering the converter input (and output) impedance appearing at terminals 1 as viewedfrom the line. This impedance is further lowered, and is made negative, by the positive feedback, which occurs in each "triode due to the connection from its plate through the RC circuit to the grid of the other triode and theconnection from the plate of that other triode through the like RC circuit to the grid of the first triode. In the circuit of each triode, and also in the converter or vacuum tube circuit as a whole, the total feedback preferably is negative, the negative feedback predominating over the positive feedback. The predominance of the negative feedback tends to stabilize the system against variation in vacuum tube constants and plate supply voltages.

Still considering Fig. 7, for example, as having terminals 1 connected in series in the line and terminals 2 connected to network ZN as shown in Fig. 10 described hereinafter, it will be appreciated that the amplifier triodes are arranged to generate in theirplate circuits a voltage, derived from the network voltage drop, which aids or boosts the line current. This aiding voltage is thus proportional to line current and will cause an increase in current over the unrepeatered condition. Because the voltage is also proportional to the network impedance, the transmission gain or current increase will be proportional to it and can be changed up or down by adjusting the network impedance up or down correspondingly.

The voltages which produce the repeater gain are obtained by feedback connection within the amplifier circuit. Voltages appearing across the network are fed back to the grids through paths comprising the coupling condensers C1 which connect the plate of each triode to the grid of the other triode. This results in a polarity or phase for the amplified network voltage which aids the current, and so this feedback is positive feedback. Voltages appearing in the cathode circuit of each tube between cathode and ground are applied to the grid in such polarity or phase that the amplified voltage appearing in the This term would be plate circuit opposes the line current. This feedback is negative feedback. The gain depends on the resultant of these two feedback voltages.

Elements in the grid circuit of each triode are used for controlling the feedback at the high and low frequencies so .as to reduce the gain outside the range of frequencies for which gain and negative impedance are desired (for example, in the case of a telephone repeater, the range of frequencies for normal telephone usage) and increase the stability of the repeater. Coupling condensers C1 and resistances R1 and R3 make combinations that reduce the positive feedback from the network at the low frequencies. Condensers C2 and resistances R3 and R1 make combinations that reduce the same feedback at the high end of the desired frequency band. As noted above, the network C1, R3 and R largely determines the value of 1 at low frequencies, and the network R3, R1 and C2 largely determines the value of 1 at high frequencies.

The network ZN supplements this frequency selective action, providing frequency selectivity in addition to that provided in the amplifier circuit. This serves to limit the gain to the transmission band of the particular circuit with which the network is designed or adjusted to be used, and thus serves to increase stability of the repeater (against singing). As explained hereinafter, the network further provides not only for adjusting the gain to any desired value within the allowable gain limits of the repeater, but also for equalizing or shaping the gain characteristic to compensate for the loss-frequency characteristics of the lines associated with the repeater, particularly in the case of non-loaded lines.

With terminals 1 in series in the line and terminals 2 connected to the impedance control network (gain control network) ZN, the repeater can be monitored and tube checks made without interfering with the conversation on the line. To facilitate such tests, preferably pin jacks J1, J2 and J3 are provided, J1 and J2 being respectively connected to the cathodes of the two triodes V1 in Fig. 7, and J3 being connected to ground (i. e., to the mid-point'of the circuit connecting the cathodes). These jacks are used for voltmeter connection in checking the cathodc-to-ground direct-current voltages of the two triode sections of the tube. These voltage tests indicate whether the tube is operating satisfactorily and whether proper voltages are being supplied. Jacks J1 and J2 are used also for connecting from either J1 or J2 to ground (13) a high impedance monitoring telephone headset (about 75,000 ohms) especially designed for the repeater. When so connected, the headset is effectively across the winding of (input and output) transformer T1 and thus monitors both directions of transmission over the line.

Any practical negative impedance converter such as that represented by Fig. 4 can be used most efficiently as a negative impedance repeater to provide gain in a transmission line either by connecting a network ZN to terminals 2 and inserting terminals 1 in series with the line, as exemplified in Fig. 10, or by connecting a network ZN to terminals 1 and shunting terminals 2 across the line, as exemplified in Fig. 11. In Figs. and 11, the line is designated 3 and the converter 4. The converter of Fig. 7 or Fig. 7A has been designed specifically for the connection of a network ZN to terminals 2 and the insertion of terminals 1 in series with the line, in the manner shown in Fig. 10. This converter will then introduce a reversed voltage type (i. e., series type) of negative impedance in series with the line. Practically one-half of the primary winding of transformer T1 should be inserted in one side of the line andthe other half of the winding should be inserted in the other side of the line, for proper balance against longitudinal currents (as shown in the case of winding 33 of Mathes Patent 1,779,382). The converter 4 may be, for example, as shown in Figs. 4, 5, 7 or 7A. The network ZN .may be, for example, as shown in Figs. 12, 13, 14 'or 18, described hereinafter.

When the converter of Fig. 7 or Fig. 7Ais used with insertion in a non-loaded line.

terminals 1 in series with a transmission line 3, the network .Zn connected to terminals ,2 tin'the zmanner shown in Fig. 10 will control the negative impedance seen .31 terminals 1 between frequencies such laSfL and ,4: indicated in 'Fig. 9, which is the band of primary interest (and thus will control the repeater gain): The preferred network for use with .the converter when the repeater is employed on voice frequency transmission lines ordinarily will not be a resistance, but will consist of some combination of resistance and capacity, or resistance, capacity and tin ductance.

Three basic forms of such networks suitable for connection to terminals 2 of Fig. 7 or Fig. 7A are presented in Figs. l2, l3 and 14. The network configuration of Fig. 12 is suitable for use with the converter when the converter is inserted in series with a coil loaded cable circuit. When the proper values are assigned to the elements of Fig. 12 this network presents an impedance that, at frequencies between about .2 and 1.1 of 'the 'cutoff frequency f5 of the periodically loaded 'cable, simulates the characteristic impedance of the inductively loaded cable circuit terminated at any point in the loading section. This network is disclosed and claimed *in my application, Serial No. 113,073, filed August 30, 1949, for Electrical Network (United States Patent 2,632,051, issued March 17, 1953). From .Zfc to 59% the network impedance closely simulates that of the line, and above .9fc the ratio of the resistive component of the network impedances to that of the line impedance is maintained sutficiently low to avoid instability. The basic section of the network comprises resistance R10 shunted by a series combination of inductance L10 and capacitance C10, and simulates approximately the characteristic impedance, as viewed at .2 loading coil. of the periodically loaded transmission line. The network is built out to full coil by adding inductance L211 in series with the basic section. A building-out capacitance C20 across the network terminal builds out the network to any fractional sectional termination desired. The component elements of the network areevaluated in terms of the inductance of the loading coil andthe capacitance and characteristic impedance of the line, andmay be adjustable for use with different line facilities or end sections.

The networks of Figs. 13 and 14, when the elements of these networks are assigned appropriate values, present impedances that, when converted into their negativesand multiplied by an appropriate numeric, are suitable for (As will become apparent further on, they are not designed to simulate characteristic 'impedances of the associated lines) Fig. 13 is useful in a negative impedance repeater for a non-loaded differs in type or length from the linesection on theother side. Elements R22, R21 and C21 are proportioned for one of the line sections, andclements R11, R12 and C12 for the other line section. Fig. 14 is useful in a negative impedance repeater when a plurality of the repeaters are used in tandem for negative impedance loading'as described hereinafter. The network of this figurecomprises two parts in series. One of these parts is composed of resistance R13 and capacitance-C13 in series, shunted by inductance L13. The other of the two parts is composed of resistance R23 and inductance L-zs, shunted by capacitance C23.

In many cases, especially within the area covering a city or town, known as an exchange area, a line that has already been loaded with periodically spaced series inductance coils to improve its transmission response, nev- .ertheless can advantageously have its attenuation reduced further by the addition of a negative'impedance inseries in the coil loaded line. Such an addition ordinarilypmduces an impedance irregularity; but in many instances this irregularity is not a serious transmission impairment in coil loaded lines and its disadvantage is more than outweighed by the gain in transmission obtained by the insertion of this negative impedance. In such cases, the negative impedance inserted inthe line preferably is similar in characteristic to the negative of. the characteristic impedance of the coil loaded line multiplied 'bya numeric which depends in value upon the return loss ofthe' 'line at the point of insertionf The negative-impedance maybe provided, for instance, by a negative impedance repeater such as that of Fig. 10, and mayy'for example, comprise the negative impedance-converter 'of Fig; 7 'or Fig. 7A with a network ZN of impedance-value Zn suchas the networkofFig. 12. f

A method of thus-applyingthe negative impedance repeater to inductively loaded 'line s'c an-be explained by the example shown in-Fig. 15, where it 'is assumed for simplicity that the two 'pe'riodically 'coil lo'aded line' sections 5 and 6 between which the negative impedance repeater 7 is connected are identically alike, the attenuation of each being taken by way 'ofexample, as 4.5 decibels. Their far end terminations maybe, for example, at central ofiices 8 and 9, respectively, which comprise centraloflice switching equipment for connecting lines 5 and 6 to other circuits, as for instance, subscriber loops including subscriber stations '10'and 11. The repeater 7 maybe, for example, at a third central 'o'ifice in 'the exchange area, this ofiice being designated 12in the drawing. The negative impedance converter of 'therepeater is designated 13. As just indicated, it may bethe converter' shown in Fig.7 or lA', for instance.-

If line section 5 be either open-circuitedat'S or shortcircuited at 8, then as thefrequency' in th'e'pass band of the line is varied the impedance Zsseen at the-repeater point (if plotted on the resistance-reactance plane) will oscillate or follow a circle which enclosesthe characteristic impedance Z0. For coil loaded exchange'circuits this impedance Z5 will go around the circle approximately once for every loading point in the line'section as Z5 is investigated over the pass band of frequencies. -If the line sectioncontains no structural or otherimpedance'irregularities, then when the line is open-circuited oi "short-circuited 'at 8 the return loss [20 log1n(1+Zs/Zo)/(lP-Z5/Zo)] expressed in decibels equals twice'the line section attenuation, or 9 decibe'ls in the example of Fig. 15'. In Fig. 16 a circle 16 is shown plotted on the normalized impedance plane, i. e.,,a resistance-reactance' 'plan'e whereon the abscissae are resistive or real components of theratio Zs/Zo, and the ordinates are reactive componentsof the ratio. In this plane the point liiO equals. the characteristic impedance Z of any line. The circle 16 is the locus of all possible values of'Zs/Zo that will give a 9-decibel return loss. As shown in Fig. 16, .for this 9- decibel return loss circle Z0 will be a minimum at 0.477; or in om n/bra s, 5 will be a minimum at 0.477Z6.' The impedance 25 will be ia maximum at 2.09Zo. Thus for any given return loss (RL') the impedance Z5 will have one minimum and one'maximum value.

Let -h designate the factor'by which the impedance ZN of network Zn must be multiplied in order to obtain the value of the negative impedance presented to'the lineby the repeater (at terminals 1 of Fig. 7 or 1A, for example).

For stability, the negativeimpedahce of the repeater (-hZN) cannot exceed -0.477Zu 2 if the line is to be either short-circuited or open-circuited 'at both ends 8 and 9, the two line sections having been assumed. to be identical. The negative impedance (-hZN) has manufacturing variations. These amount to about per cent so that the allowable negative impedance must be reduced by 10 per cent. Hence hZN cannot exceed 0.429Zo 2 or 0.858Zo. r

If, in the talking connection, the return loss at 8 of the subscriber loop including station 10, and the return loss at 9 of the subscriber loop including station 11 each b assumed to be 6'decibels, forexample, then both Z5 and Zs'follow the IS-decibel return loss circle 17 shown in Fig. 16 when the line'is connected for subscriber use.

' Thevariation' in the insertion gain characteristic over the band of frequencies transmitted can be computed as follows. From the IS-decibel return loss circle it canfib'e seen that the minimum value of impedance which Zscan have during the talking condition of the circuit is 0.696Z0 and the maximum value is v1.43Zu. If the negative impedance (hZn') of 0.858Zo is inserted in this circuit the maximum and the minimum value of insertion gain can be found by substitution in the following equationz' Gain in de0ibels= 20 log 1 min 5+ t The maximum value is 8.3 decibels and the minimum value 3.l decibels. The effective insertion gain, therefore.

peaters thisreduction is slightly less than one-half. For' intermediate repeaters it may be'slightly more, as has just been shown.

It is noted that the negative impedance repeater introduces appreciable variation in transmission frequency response. Repeaters of the 22-type, in common use, likewise introdnce such variation (though the fact is perhaps not generally appreciated).

Fig 17" shows a negative impedance repeater 27 connecting 'inseries a coil'loaded line 25 and anon-loaded line 26. The repeater 27 may be at a central ofiice 22. The lines 25 and 26 may connect central ofiices 28 and 29, for example, which may comprise switching equipment (not shown) for connecting lines 25 and 26 to other circuits, as for instance, subscriber loops (not shown). The centraloffices 22,28 and 29 may be all in the same exchange area. In many cases, especially within an exchange area, a circuit comprising a coil loaded line (such as 25) and-a non-loaded line (such as 26) in tandem can advantageously have the attenuation of the circuit reduced by connection of a-negative impedance (such as 27) in series between the lines, as in Fig. 17,- for example. In Fig. 17 the negative impedance repeater 27 may be, for instance, of the type shown in Fig. 10,.and may, for example, comprise a negative impedance. converter 13 of thetype shown in Fig. 7 or Fig. 7A, with a network ZN such as the network shown in Fig. 18.

:The network Zn in Fig. 18 comprises two networks 31 and 32 in series. The network 31 is shown as the network of Fig. 12 and is determined by the return loss of the loaded line 25. The network 32 is determined by the line constants per unit length and the length of the non-loaded line 26. This network 32 may be, for example, the net- .work shown in Fig. 13 as composed of elements R11, R12 and C12.

It is to be understood that the above-described arrangements are illustrative of the application of the principles of the invention. Numerous other arrangements may be devised by those skilled in the art without departing from the spirit and scope of the invention.

What is claimed is:

w I 1. In combination, a negative impedance converter which comprises an'amplifying device having an anode, a cathode, and a control grid, a first direct current circuit path exclusive of said anode between said control grid and'said cathode, a second directcurrent circuit path exclusive of said control grid between said anode and'said cathode, a first inductance coil common to both of said circuit paths and forming a negative feedback impedance, :1 second inductance coil :in said second circuit path in serial relation with said first coil, and a positive feedback path including means to supply to said control grid a voltage proportional to but reversed in phase from the voltage appearing across said second coil, the voltage amplification factorof said device and the product of said voltage amplification factor and the feedback factor of said positive feedback path both being many times greater than unity, a first terminating circuit coupled in parallel with said first coil, and a second terminating circuit coupled in parallel with said second coil, the impedance presented to either one of said terminating circuits by said converter being related to the impedance presented to said converter by the other of said terminating circuits substantially by the factor k, where k is substanially a numeric over a predetermined operating frequency range.

2. In combination, a negative impedance converter which comprises an amplifying device having an anode, a cathode, and a control grid, a first direct-current circuit path exclusive of said anode between said control grid and said cathode, a second direct-current circuit path exclusive of said control grid between said anode and-said cathode, a first inductance coil common to both .of said circuit paths and forming a negative feedback impedance, a second inductance coil in said second circuit path in .serial relation with said first coil, and a positive feedback path including means to supply to said control grid a voltage proportional to but reversed in phase from the voltage appearing across said second coil, a first terminating circuit, means coupling said first terminating circuit in parallel with said first coil, a second terminating circuit, and means coupling said second terminating circuit in parallel with said second coil, the impedance presented to either one of said terminating circuits bysaid converter being related to the impedance presented to said converter by the other of said terminating circuits substantially by the factor (m- #z-iwhere #2 is the amplification factor of said device and a1 is the product of a2 times the ratio of the voltage fed back to said control grid by said positive feedback path to the voltage appearing across said second coil, both 2 node, a first impedance common to both of said circuit paths and forming a negative feedback element, a second impedance in said second circuit path in serial .relation with said first impedance, and a positive feedback path including means to supply to said control electrode a voltage proportional to but reversed in phase from the voltage appearing across said second impedance, the amplification factor of said device and the product of said amplificaton factor and the feedback factor of said positive feedback path both being at least several times greater than unity, a first terminating circuit parallel-coupled to said first impedance, and a second terminating-circuit parallel-coupled to said second impedance, the impedance presented to either one of said terminating circuits by said converter being related to the impedance presented to said converter by the other of said terminating circuits substantially by the factor k, where k is 16 substantially a numeric over a predetermined operating frequency range.

4. In combination, a negative impedance converter which comprises :fiist and second amplifying devices connected ,in push-pull relation, each of said devices having an :anode, atcathode, and a control grid, a first industance coil connected between the cathodes of said devices and forming 'a negative feedback impedance, a second inductance coil connected between the anodes of said devices, ,a source of direct current for said devices connected :between ithe mid-point of said first coil and the mid-point of said second coil, respective resistive connections from the control :grids of said devices to said midpoint of said jfirst coil, and respective positive feedback paths opaque to direct current connected between the anode, of ,said first device and the control grid of said second device and between theanode of said second device and :the control grid of said :first device, the voltage amplification factorsof each of said devices and the product'of each of said voltageamplification factors and each of the feedback factors of said positive feedback paths each being :many times greater .than unity, a first terminating circuit coupled across said first coil, and a second terminating circuit coupled across said second coil, the impedance presented to either one of said terminating circuits by said converter being related to the impedance presented to said converter by the other of said termi- .nating circuits substantially by the factor k, where k is substantially a numeric over a predetermined operating frequency range.

5. In combination, a .negative impedance converter which comprises first and second amplifying devices con- ;nected in push-pull relation, each of said devices having .an anode, acathode, and a-control grid, a first inductance coil connectedbetweenthe cathodes of said devices and forming a negative feedback impedance, a second inductance coil connected between the anodes of said devices, a source of direct current for said devices connected between the .mid-point of said first coil and the mid-point of said second coil, respective resistive connections from the control grids of said devices to said mid-point of said first coil, .and respective positive feedback paths opaque to direct current connected between the anode of said first device and the control grid of said second device and between theanodeof said second device and the control grid -of said first device, a first terminating circuit coupled across said first coil, and a second terminating circuit coupled across said second coil, the impedance presented .toei'therrone of said terminating circuits by said converter beingrelated to the impedance presented to said converter by the :Other of said terminating circuits substantially by the factor where an is the amplification factor of each of said devices and his the product of 2 times the ratio of the voltage fed back to .the respective control grids of said devices by said positive feedback paths to the voltage appearing across each half of said second inductance coil, both a and n being many times greater than unity over a predetermined qperating frequency range.

current-receiving electrodes of said devices, a source of direct current for said devices connected between the mid point of said first impedance and the mid-point of said secondimpedanceQrespectiVe resistive connections from 17 the control electrodes of said devices to said mid-point of said first impedance, and respective positive feedback paths opaque to direct current connected between the current-receiving electrode of said first device and the control electrode of said second device and between the current receiving electrode of said second device and the control electrode of said first device, a first terminating circuit coupled across said first impedance, and a second terminating circuit coupled across said second impedance, the

forming a negative feedback impedance, a second inductance coil connected between the anodes'of said devices, a source of direct current for said devices connected between the mid-point of said first coil and the mid-point of said second coil, respective resistances bypassed by capacitors connected from the control grids of said devices to said mid-point of said first coil, and respective positive feedback paths each comprising a capacitor in series with a resistance connected between the anode of said first device and the control grid of said second device and between the anode of said second device and the control grid of said first device, a. first terminating circuit coupled across said first coil, and a second terminating circuit coupled across said second coil, the impedance presented to either one of said terminating circuits by said converter beingrelated to the impedance presented to said converter by the other of said terminating circuits substantlally by the factor k, where k is substantially a numeric over a predetermined-operating frequency'range.

8. A four-terminal negative impedance converter which comprises first and second amplifying devices connectedv in push-pull relation, each of said devices having an anode, a cathode, and a control grid, a first inductance coil connected between the cathodes of said devices and forming a negative feedback impedance, a second inductance coil connected between the anodes of said devices, a source of direct current for said devices connected between the mid-point of said first coil and the mid-point of said second coil, respective resistive connections from the control grids of said devices to said mid-point of said first coil, respective positive feedback paths opaque to direct current connected between the anode of said first device and the control grid of said second device and between the anode of said second device and the control grid of said first device, the voltage amplification factors of each of said devices and the product of each of said voltage amplification factors and each of the feedback factors of said positive feedback paths each being many times greater than unity, a first pair of terminals coupled to the respective cathodes of said devices, and a second pair of terminals coupled to the respective anodes of said devices, the impedance presented by either pair of said terminals being related to any impedance connected across the other pair of terminals substantially by the factor k, where k is substantially a numeric over a predetermined operating frequency range.

9. A four-terminal negative impedance converter which comprises first and second amplifying devices connected in push-pull relation, each of said devices having an anode, a cathode, and a control grid, a first inductance coil connected between the cathodes of said devices and forming a negative feedback impedance, a second inductance coil connected between the anodes'of said devices, a source of direct current for said devices connected between the mid-point of said first coil and the mid-point of said second coil, respective resistances bypassed by capacitors connected from the control grids of said devices to said mid-point of said first coil,- respective positive feedback paths each comprising a capacitor in series with a resistance connected between the anode of said first device and the control grid of said second device and between the anode of said second device and the control grid of said first device, a first pair of terminals coupled to the respective cathodes of said devices, and a second pair of terminals coupled to the respective anodes of said devices, the impedance presented by either pair of said terminals being related to any impedance connected across the other pair of terminals substantially by the factor k, where k is substantially a numeric over a predetermined operating frequency range.

10. A four-terminal negative impedance converter which comprises first and second amplifying devices connected in push-pull relation, each of said devices having a current-emissive electrode, acurrent-receiving electrode,

and a control electrode for current passing between said' current-emissive electrode and said current-receiving electrode, a first impedance connected between the currentemissive electrodes of said devices and forming a negative feedback element, a second impedance connected between the current-receiving electrodes of said devices, a source of direct current for said devices connected between the midpoint of said first impedance and the mid-point of said second impedance, respective resistive connections from the control electrodes of said devices to said midpoint of said first impedance, respective positive feedback paths opaque to direct current connected between the current receivingelectrode of said first device and the control electrode of said second device and between the current-receiving electrode of said second device and the control electrode of said first device, a first pair of terminals coupled to the respective current-emissive electrodes of said devices, and a second pair of terminals coupled to the respective current-receiving electrodes of said devices, the impedance presented by either pair of said terminals being related to any impedance connected across the other pair of terminals substantially by the factor k, where k is substantially a numeric over a predetermined operating frequency range.

References Cited in the file of this patent UNITED STATES PATENTS 

